Roots of Reason
rootsofreason.org
Stuck? Scan for the anchor chart
What Division Means · Set 4 · Grade 3
Rates: The "For Each" Question
Some numbers come in pairs: miles with hours,
dollars with pencils. Division finds what one gets.
dollars with pencils. Division finds what one gets.
A bike rider goes
12 miles in 3 hours
divide by the hours ↓
12 ÷ 3 = 4 miles each hour
the rate: what one hour gets
4 mi
hour 1
4 mi
hour 2
4 mi
hour 3
Same trip, cut into equal hour-boxes. Every "for each" problem is an equal-groups problem.
Words to look for: each, per, every one. When you see them, the problem may call for division.
Roots of Reason
Rates · Set 4
Name
Date
Fill the Hour Boxes
A steady walker covers 10 blocks in 2 hours.
Same speed the whole time. How far in one hour?
Same speed the whole time. How far in one hour?
1.Here are the 10 blocks as dots, and the 2 hour boxes. Deal the blocks into the boxes evenly: draw 1 dot in a box, cross one off, repeat.
hour 1
hour 2
10 ÷ 2 = blocks each hour
2.A bakery oven bakes 12 rolls in 3 batches, the same number every batch. Draw the batches as boxes yourself this time, deal the rolls in, and finish the sentence.
Each batch has rolls. 12 ÷ 3 =
Roots of Reason
Rates · Set 4
Name
Date
The Price for One
Stores sell things in packs. Division tells you
what you are really paying for each one.
what you are really paying for each one.
1.A pack of 4 juice boxes costs 8 dollars. Share the 8 dollar-coins under the 4 juice boxes so every box gets the same. Draw the coins in.
box 1
box 2
box 3
box 4
One juice box really costs dollars.
2.Which deal is better? Store A: 3 stickers for 6 dollars. Store B: 5 stickers for 5 dollars. Find the price for one sticker at each store first. No fair guessing.
Store A: 6 ÷ 3 = each
Store B: 5 ÷ 5 = each
Circle the better deal:
Store A
Store B
Roots of Reason
Rates · Set 4
Name
Date
Which Number Do I Divide By?
Divide by the thing that comes after the word "each."
"Miles each hour" means divide by the hours.
"Miles each hour" means divide by the hours.
1. A train goes 90 miles in 3 hours. You want: miles each hour. Circle what to divide by, then solve.
90
3
=
2. A reader finishes 40 pages in 5 days. You want: pages each day.
40
5
=
3. Trickier: a garden hose fills 6 buckets in 30 minutes. You want: minutes each bucket. Check which way to divide.
30 ÷ 6
6 ÷ 30
=
4.Write your own "each" problem for the division fact 18 ÷ 6 = 3. Draw a small picture to go with it.
Roots of Reason
Rates · Set 4
Name
Date
Rate Hunt
Rates are on price tags, cereal boxes, speed signs
and game scores. Find one outside of school.
and game scores. Find one outside of school.
1.Show your rate: a photo of the tag or sign, or draw what you saw.
or draw it here
2.Tell your rate's story in numbers:
I found for .
So each one is ÷ =
Example: 6 granola bars for 12 dollars. Each bar is 12 ÷ 6 = 2 dollars.
Roots of Reason
rootsofreason.org
What Division Means · Set 4 · Grade 3
Answer Key and Teacher Notes
Fill the Hour Boxes (page 2)
1. 10 ÷ 2 = 5 blocks each hour 2. Each batch has 4 rolls; 12 ÷ 3 = 4
The Price for One (page 3)
1. 2 dollars per box 2. Store A: 2 each; Store B: 1 each; better deal: Store B
Which Number Do I Divide By? (page 4)
1. Divide by 3: 90 ÷ 3 = 30 2. Divide by 5: 40 ÷ 5 = 8 3. 30 ÷ 6 = 5 minutes per bucket 4. Any story with 18 things shared over 6 "eaches"
Rate Hunt (page 5)
Answers vary. Check the division runs total ÷ count, and the units in the answer say "per one": dollars per bar, miles per hour, points per game.
Page 4 problem 3 is the one to watch: "minutes per bucket" flips the division, and students who divide without reading the units will write 6 ÷ 30. What helps is asking out loud: what should one bucket get? A student who can ask that question is ready for unit rates in grade 6.